Quantitative Measures of Solvent Polarity - ACS Publications

Chem. Rev. 2004, 104, 175−198

175

Quantitative Measures of Solvent Polarity Alan R. Katritzky,* Dan C. Fara, Hongfang Yang, and Kaido Ta¨mm Center for Heterocyclic Compounds, Department of Chemistry, University of Florida, Gainesville, Florida 32611

Tarmo Tamm and Mati Karelson Department of Chemistry, University of Tartu, 2 Jakobi Street, Tartu 51014, Estonia Received May 20, 2003

Contents 1. Introduction 2. Individual Solvent Scales 2.1. Brief Historical Overview of Development of Scales 2.2. Types of Properties Used To Define Solvent Polarity Scales: Division into Major Classes and Definitions 2.2.1. Equilibrium and Kinetic Measurements 2.2.2. Spectroscopic Measurements 2.2.3. Multiparameter Approaches 2.3. Detailed List of Solvent Scales with References and Number of Solvents 2.4. Attempts To Relate Scales to Descriptors 3. Interrelations between Solvent Scales 3.1. Correlation of Solvent Scales 3.2. Overall Dimensionality of Solvent Parameters 3.2.1. General Statistical Approaches 3.2.2. Principal Component Analysis (PCA) Approach 4. Summary and Future Work 5. References

175 177 177 182 182 183 186 189 190 192 192 193 193 193 196 196

1. Introduction In 1890, W. Ostwald wrote: Almost all the chemical processes, which occur in nature, whether in animal or vegetable organisms or in non-living surface of the Earth ... take place between substances in solution. Simplistically, “solutions” can be defined as homogeneous liquid phases consisting of more than one substance in variable ratios, where one of the substances, the so-called “solvent” (which could itself be a mixture), is treated differently from the other substances, which are called “solutes”. Usually, the solute(s) is/are the minor component(s) and the solvent is the component in excess. In 1862, Berthelot and de Saint-Giles, after thorough studies on the esterification of acetic acid with ethanol, noted for the first time the influence of solvents on the rates of chemical reactions.1 In 1890, Menschutkin asserted that a reaction cannot be

separated from the medium in which it has occurred.2 He considered that the influence of solvents is primarily related to their chemical structure rather than their physical properties and postulated relationships between the rates of reactions and solvent structure. Later, it became obvious that a solvent should not be considered only as a macroscopic continuum characterized purely by physical constants but also as a discontinuum consisting of individual mutually interacting solvent molecules. These macroscopic and microscopic approaches must be considered together (not separately) as defining the general concept of “solute-solvent interactions”. This concept involves and influences all of the following: (i) macroscopic (bulk) physical properties, including refractive index, relative permittivity, density, thermodynamic characteristics and more; (ii) microscopic intermolecular forces, including ion-dipole, dipole-dipole, dipoleinduced dipole, hydrogen bonding, electron pair donor-electron pair acceptor interactions (EPD/ EPA), and solvophobic interactions; (iii) solvation in multicomponent systems, involving selective solvation and micellar solvation (solubilization); and (iv) “chemical” solvation related to ionization and dissociation processes. Factors i-iv are collectively well-known as “solvent effects” and are conventionally ascribed to a solvent’s “polarity”. The term “polarity” is usually related to the capacity of a solvent for solvating dissolved charged or dipolar species. “Polarity” is easy to comprehend qualitatively, but substantial difficulties arise with (i) its precise definition and (ii) its quantitative measurement. Reichardt3 defined “solvent polarity” as “the overall solvation capability (or solvation power) for reactants and activated complexes as well as for molecules in the ground and excited states, which in turn depends on the action of all possible, specific and nonspecific, intermolecular forces between solvent and solute molecules, including Coulomb interactions between ions, directional interactions between dipoles, and inductive, dispersion, hydrogen-bonding, and chargetransfer forces, as well as solvophobic interactions. Only those interactions leading to definite chemical alterations of the solute molecules through protona-

10.1021/cr020750m CCC: $48.50 © 2004 American Chemical Society Published on Web 01/14/2004

176 Chemical Reviews, 2004, Vol. 104, No. 1

Alan Katritzky is the Director of the Florida Center for Heterocyclic Compounds at the University of Florida, where he has been Kenan Professor of Chemistry since 1980. His research encompasses heterocyclic chemistry, synthetic methodology, quantitative structure−property relationships, and many areas of mechanistic and applied organic chemistry. His honors include 11 honorary degrees from 8 countries and membership in 5 foreign Academies. Details of these and his extensive publications are given on his home page at http://ark.chem.ufl.edu. Recently he founded a not-for-profit foundation “Arkat-USA inc”, which publishes the electronic journal Arkivoc (Archive for Organic Chemistry) completely free to readers and authors (see Web page at http://arkat-usa.org).

Katritzky et al.

Hongfang Yang, born in Taiyuan, Shanxi, China, obtained her B.S. degree from Wuhan University in 1996. Subsequently, she joined the Chemistry and Chemical Engineering College of Lanzhou University for graduate studies under the supervision of Professor Xinfu Pan and received her M.S. degree in 2000. Currently, she is a Ph.D. student with Dr. Alan R. Katritzky in the Chemistry Department of the University of Florida. Her major research interest is to develop methodology to synthesize heterocyclic compounds that are of pharmaceutical and medicinal interest.

Kaido Ta¨mm, born in Tartu, Estonia, received his M.S. degree in chemistry at the University of Tartu, in 2001. In 2002 he joined Prof. Alan R. Katritzky’s computational chemistry group at the University of Florida. Dan C. Fara, born in 1967 in Caransebes, Romania, received his M.S. degree in “Organic compounds with biologic activitysQSAR” at the West University of Timisoara, Romania, in 1997. Since 2001, he has been a Ph.D. student in molecular engineering at the University of Tartu, Estonia, and also chemist researcher at the University of Florida. His research interests are related to various applications of the QSAR/QSPR method.

tion, oxidation, reduction, complex formation, or other chemical processes are excluded.” This definition already suggests that solvent polarity cannot be uniquely assessed quantitatively by any single physical constant. Furthermore, Reichardt demonstrated experimentally3 that macroscopic dielectric constants alone are unsuitable measures of molecular-microscopic interactions. From a very general point of view, the chemical processes (i.e., the protonation by solvent) may also substantially modify the solvational capability (or solvational power) of solvents. Therefore, we would expand Reichardt’s definition of solvent polarity and do not exclude such phenomena in the further discussion. A most important feature for the success of any planned reaction is the selection of a suitable solvent: solvents influence both chemical reactivity and reaction rates. The importance of solvent effects has

long stimulated attempts to define solvent polarity in terms of empirical parameters, based on diverse solvent-sensitive reference processes. The aims of such attempts have been to obtain better parameters of solvent polarity by choosing solvent-dependent standard systems and examining the changes in parameters of that system when the solvent is changed.3 Solvents can be classified in many ways including their polarity, acidity, electron pair or proton-donating properties, etc. Some solvent scales are defined to describe individual intermolecular interactions in liquid media; others do not separate specific properties and are referred to as general polarity scales. The present paper focuses on available quantitative measures of solvent polarity. It reviews the different individual solvent scales (developed using pure solvents and based on empirical parameters) and the interrelations among them. The last section summarizes briefly the present position and the potential for future development of the concept of solvent polarity.

Quantitative Measures of Solvent Polarity

Tarmo Tamm (born in 1974) is a lecturer at the Institute of Physical Chemistry at the University of Tartu, Estonia. His research interests have been related to the properties and quantum chemical modeling of conducting polymers (Ph.D. degree in 2003) and the applications of QSAR/ QSPR to the properties of solutions.

Mati Karelson (born in 1948) is Professor and Head of Theoretical Chemistry at the University of Tartu, Estonia. He received his Ph.D. degree in physical organic chemistry in 1975. His research has dealt with the theory of solvent effects, the foundations of QSAR/QSPR, and the development of the corresponding computer software. He is actively engaged in teaching, industrial consulting, and scientific management. He is also Courtesy Professor in Chemistry at the University of Florida.

Chemical Reviews, 2004, Vol. 104, No. 1 177

of solvent scales were made by Kosower,5-7 Katritzky and co-workers,8 Koppel and Palm,9 Gutmann and Wychera,10 Dimroth and Reichardt,11 Kamlet and Taft,12-14 Abraham,15 and many others (see Table 1). Choosing a model system and recording the response of one of its parameters to the change of solvent have been the essence of the development of most of these scales. The model process must be chosen with care and represent properly the interactions of the system, yet no one scale can be universal and useful for all kinds of reactions. On more theoretical considerations, the best model processes maximize solvent effects. According to Abboud and Notario,16 the “empirical treatment” of solvent polarity is frequently assisted by the regularities displayed in many cases by solvent effects. Many examples of processes known to be solventsensitive cannot be correlated by a single empirical solvent parameter. It has been found repeatedly that the simple concept of “polarity” as a universally determinable and applicable solvent characteristic is a gross oversimplification. The solvation capability or solvation power of a solvent, which has been roughly divided into nonspecific and specific solutesolvent interactions, is the result of many different kinds of interaction mechanisms between the molecules of the solute and the solvent. By considering a solute, SOL, and two different properties, P1 and P2, with the values {P10, P11, ..., P1i, ...} and {P20, P21, ..., P2i, ...}, respectively, in solvents S0, S1, ..., Si, ..., a solvent scale can easily be constructed. Choosing S0 as a reference solvent, taking for each solvent, Si, the difference Pi ) (P1i P10) could be considered to define a simple scale. If the property P1 is a “good descriptor” of solvent effects on P2, eq 1 or 1a holds for solvent Si, wherein k is a constant independent of the solvents and determined only by P2. Then pi is the “solvent parameter” characteristic of solvent Si.

2. Individual Solvent Scales

P2i - P20 ) k(P1i - P10)

(1)

P2i - P20 ) kpi

(1a)

or

2.1. Brief Historical Overview of Development of Scales The term “solvent polarity” lacks an exact definition, but it is generally used to encompass all of the intermolecular interactions of which the solvent is capable. During the past few decades, it became clear that the use, for example, of Clausius-Mossotti relative permittivity alone cannot represent completely the electrostatic solute-solvent interactions and, thus, cannot provide a reliable guide for predicting solvent effects on specific chemical reactions. Consequently, many different alternatives were proposed to measure solute-solvent interactions, resulting in a large variety of so-called “solvent polarity scales” based on diverse solvent-sensitive reference processes/empirical parameters. Historically, the forerunners in the development of empirical scales were Grunwald and Winstein,4 who in 1948 computed Y values from rate constant studies. Significant contributions to the development

Such an equation can be applied only to data for a large number of well-chosen solvents, and its success must be examined by proper statistical methods. The separation of solvent polarity into various solutesolvent interaction mechanisms is purely formal and may not be even theoretically valid as the interactions could be coupled and not operate independently of each other. However, if such a separation could be justified, the resultant parameters could be used to interpret solvent effects through such multiple correlations and provide information about the type and magnitude of interactions with the solvent. In such a case, only applications to processes that have the same relative sensitivity to various interaction mechanisms as the single solvent parameter will give a good correlation. Such multiparameter approaches to explain solvent effects on chemical and physical properties have been proposed by Katritzky et al.,8


Katritzky et al.

Table 1. Solvent Scales Used in the Study scalea

no.

no. of solventsb

author(s)c

Spectroscopic Measurements acceptor number, derived from 31P NMR of triethylphosphine oxide in different solvents

1

AN

34

Mayer

2

AN

52 31

Marcus Knauer and Napier

3

B

71

Koppel and Palm

4

B′

19

Renge and Avarmaa

5

B-2

53

Koppel and Paju

6

BCo

25

Waris

7

BKT

44

Krygowski

8

BPe

25

Waris

9

Co

12

Nakajima

10

Cp-SCS

25 6

Waris Bromilow

11 12 13

CTTS Cu-λmax DCo

16 38 23

14

DS

61

15 16

E(NR) E*MLCT

82 33

17

ECT(π)

28

18 19

E° (H2(g)/H+(aq) EB

6 53

20

ECT (A)

23

21

ELMCT

6

22

ET(30)

362

23 24 25 26

SO

ET G H 2 J119Sn-117Sn

36 21 11 21

27

K

25

28

KqMMA

12

29

log γKc

11

30 31

m* NCo

10 25

32

Ov

25

33 34

pKBH+ Ps

35 36

Py Qf

94 12

37

Qm

52

38

SA

121

10 108

physical background

N14 hyperfine splitting constants of di-tert-butylnitroxide free radical basicity from stretching frequency of CH3OD in different solvents O-H stretching frequency shift in cm-1 in phenol dissolved in CCl4 when a nucleophile is added to form an H-bonded complexes acid-base hydrogen bond formation induced shifts of phenol OH group stretching frequency ratio of the fluorescence intensities of bands I and III of the vibronic spectra of benzo(R)coronene calculated from the difference of the longest wavelength band in the UV-vis spectra measured for p-nitroaniline and N,N-diethyl-p-nitroaniline relative band intensities (I/III) for benzo[ghi]perylene fluorescence spectra relative band intensities (I/III) for coronene fluorescence spectra

substituent chemical shifts for the para carbon of N,Ndimethyl for the monosubstituted (n ) 21) benzene Fox and Hayon absorption maxima of iodide ions Persson maximum absorption band of Cu(tmen)(acac)(solv) Waris ratio of the fluorescence intensities of bands I and IV of the vibronic spectra of dibenzo[R,j]coronene Persson donor strength decrease in symmetric stretching frequency of Hg2Br2, between the gas phase and solutions Deye and Berger Nile red transition energy Manuta and Lees solvent dependence of metal to ligand charge-transfer absorption maxima of W(CO)4 with 1,10-phenanthroline Kaim CT spectra of W(CO)4 complexes with TCNE E*MLCT (cm-1) ) 3000 (cm-1) × ECT(π) + 12360 (cm-1) Persson standard electrode potentials in volts of [H2(g)/H+(aq)] Janowski energy of nfp* transition in the 2,2,6,6tetramethylpiperidine N-oxyl spectrum Davis UV charge-transfer absorption maxima of tetran-hexylammonium iodide trinitrobenzene Shepherd energies of charge-transfer transitions of (CN)5FeL2- and imidazole complexes Reichardt molar electronic transition energy of dissolved negatively solvatochromic pyridinium N-phenolate betaine dye Walter and Bauer UV-vis spectra of N,N-(dimethyl)thiobenzamide-S-oxide Allerhand and Schleyer infrared vibration shift of hydrogen bonding Mukerjee molar concentration of OH dipoles in (55.4 M) TEMPO Lockhart tin-tin spin-coupling constant 2J(119Sn-117Sn) of the hexaorganodistannoxanes Menger and Boyer equilibrium constants for the conformational mobile (+)-trans-a-chloro-5-methylcyclohexanone Fouassier and Jacques quenching rate constants for the deactivation of triplet thioxanthone by methyl methacrylate Pac fluorescence quenching rate constants for naphthonitrile-olefin and furan pairs Bagno and Scorrano NMR chemical shift of free base and protonated base Waris ratio of fluorescence intensities of bands I and III of vibronic spectra of naphtha[2,3-R]coronene Waris relative band intensities (I/III) for ovalene fluorescence spectra Bagno and Scorrano NMR chemical shift of free base and protonated base Middleton bathochromic UV-vis spectra shifts of λmax of (R-perfluoroheptyl-β,β-dicyanovinyl)aminostyrenes Dong and Winnik relative band intensities I1/I3 for pyrene fluorescence spectra Abdel-Mottaleb fluorescence properties of 7-hydroxy-4-methylcoumarin laser dye Marvel heat of mixture of chloroform with solvents by infrared spectra Catalań and Dıáz solvent acidity, evaluated from UV-vis spectra of o-tertbutylstilbazolium betaine dye and its nonbasic homomorph o,o′-di-tert-butylstilbazolium betaine dye

refsd 75 14 76 9 77 55 78 79 80 81 78 82 83 84 78 38 85 86 87 84 88 89 90 62 91 39 92 93 94 95 96 97 78 80 97 98 99 100 101 102



Table 1 (Continued) no.

scalea

no. of solventsb

author(s)c

39

SB

202

Catalań

40

SPP

100

Catalań

41 42 43

SPPN Tex XX Z

6 19 31

44 45

R β

185 185

46

π*

229

47 48 49

π*aso χR ∫C6H5F

29 58 24

50 51 52 53

∫HP-NO2 ∫Npyrrole δLi+ ∆

29 13 11 55

54 55 56

δ0 ∆1-Et ∆R

15 23 36

57 58 59 60

∆δCHCl3 ∆υA ∆υD θ1K

28 30 92 80

61

θ2K

80

62

λ

24

63 64 65

λAMNPS λAMS λANa

6 14 7

66 67

λFMHN12 π1*

21 96

68

π2*

72

69

πAV

19

70 71 72

τ υa-υm υC

9 12 32

73 74 75 76 77 78 79 80

υCE ΦfBBVB φfCEA χB s ∆νCI ∆νOH -σoλ

22

81

CB

123

82 83

D1 DH

18 24

Eliel and Hofer Persson

84

DN

66

Marcus

85

E(H-bond)

13

Banerjee

8 12 16 68 68 16

physical background Spectroscopic Measurements (Continued) solvent basicity, evaluated from UV-vis spectra of 5-nitroindoline and its nonacid homomorph 1-Me-5-nitroindoline calculated from UV-vis spectra of 2-(dimethylamino)-7nitrofluorene and its homomorph 2-fluoro-7-nitrofluorene

Fujita David and Hallam Marcus

hydroxyl proton exchange time at 30 °C solvent-induced frequency shifts of SO2 transition energies for charge-transfer band of complex from 1-ethyl-4-methoxycarbonylpyridinium iodide Marcus solvatochromic parameter of solvent HBD (hydrogen-bond donor) acidity Marcus solvatochromic parameter of solvent HBA (hydrogen-bond acceptor) basicity Laurence solvatochromic parameter: index of solvent dipolarity/polarizability, which measures the ability of the solvent to stabilize a charge or a dipole by virtue of its dielectric effect Buncel and Rajagopal bathochromic shifts of six azo merocyanine dyes Brooker transition energy of merocyanine dye (VII) 19F NMR shielding parameters of fluorobenzene in infinitely dilute Taft solutions relative to fixed external standard (20% p-difluorobenzene in CCl4) 19 Taft F NMR shielding parameters in p-nitrofluorobenzenes Witanowski nitrogen NMR shieldings of pyrrole referred to neat nitromethane Popov chemical shifts of Li nucleus in different solvents Gurka and Taft difference of 19F nucleus shifts of p-fluorophenol between that in solvents and that in carbon tetrachloride 23 Bloor and Kidd Na chemical shifts of sodium iodide in different solvents Anderson and Symons internal shift of 1-ethyl group of 1,4-diethylpyridinium Anderson and Symons difference between the 2,6- and 3,5-ring proton shift of 1,4-diethylpyridinium Hahn shift of pure chloroform relative to that of chloroform in dilute solution Kagiya perturbation of solvents on the CdO vibration band of acetophenone Kagiya perturbation of solvents on O-D vibration band of methanol-d Sjo¨stro¨m and Wold polarity of solvent, based on PCA combined with a cross-validation technique of solvatochromic shift data Sjo¨stro¨m and Wold polarizabiliy of solvent, based on PCA combined with a cross-validation technique of solvatochromic shift data Thomas maximum absorption of electronic spectra of heteroleptic molybdenum complexes Raileanu absorption maxima for MNPS Catalań absorption band maxima for MS Toma and Takasugi maximum absorption wavenumbers for charge-transfer bands of Na3(acpy)Fe(CN)5 Catalań fluorescence band maxima for MHN12 Abe calculated from the frequency shifts of the electronic absorption spectra of N,N-dimethyl-4-nitroaniline Abe calculated from the frequency shifts of the electronic absorption spectra of naphthalene Taft aromatic 13C NMR shifts induced by protonic solvents in a solution of benzotrifluoride and phenylsulfurpentafluoride Sukowski vibrational cooling times of azulene by ps spectra study Werner and Rodgers Stoke shift of fluorescence spectrum of N,N-diethyl-9-anthramide Catalań wavenumber of first UV-vis absorption maximum of chromophore Me2NT2NO2 Lark relative infrared frequency shifts for chloroethane El-Daly fluorescence quantum yield of BBVB Saito fluorescence quantum yield of coelenteramide Brooker transition energy of merocyanine dye (IV) Fox and Hayon static dielectric constant Laurence IR frequency shifts of iodine cyanide C-I bonds Laurence IR frequency shifts of phenol hydroxyl group Fox and Hayon absorption maxima of solvated electrons Drago

Equilibrium Measurements susceptibility to covalent interaction of a base statistical from ∆H data of different bases and acids ∆G° between cis- and trans-2-isopropyl-5-methoxy-1,3-dioxane ∆G of transfer of Na+ from solvent to reference solvent (1,2-dichloroethane) for hard acceptors donor number, negative ∆H value for 1:1 adduct formation between SbCl5 and solvent molecules in dilute solution of 1,2-dichloroethane calculated E(H-bond) values from the enthalpies of solvent for seven solute-solvent systems

refsd 57 48 103 104 14 14 14 47 49 105 106 107 108 109 110 111 112 112 113 53 53 114 114 115 116 117 118 117 51 51 119 120 121 122 123 124 125 105 83 126 126 83 127 128 38 14 129


Katritzky et al.

Table 1 (Continued) scalea

no.

no. of solventsb

86

E1/2U

87

EBB

88

Eenzyme

89 90 91

HClsol log Kf Log KsNa-L

21 6 10

92

PA

20

93

Sp

13

94 95

Sp,enzyme SS, enzyme

17 20

96 97

X ∆acidH

28 63

98

∆Gtwfs

12

99

∆Gt0(TPA)

10

100 101

∆HMIm ∆HPS

22 8

102 103 104

∆Hυ ∆SS° ∆H°solv

22 9 36

105

ε0

31

106

Ω

36

107

-∆H0

76

108

µM

34

109 110 111 112

BINAP-τiso BINAP-τor Dπ K4-nitro-deaab

15 15 34 10

113 114 115

KDC KETC° Kion

24 9 11

116

KPhNH2/BO

14

117 118

Kq Kr

27 10

119 120

Log(K)EDBT NBS

5 12

121 122

NT Rp

6 20

123

Y+

6

124 125 126 127

Y1-OTr Y2-OTr YBr YCl

5 5 5 5

9 123

BF3

9

author(s)c

physical background

Equilibrium Measurements (Continued) Seeber and Zanello formal electrode potentials for the couple UIV-UV in different solvents Drago susceptibility to electrostatic interaction of a base statistical from ∆H data of different bases and acids Fitzpatrick and Klibanov enantioselectivity of subtilisin Carlsberg in transesterification reaction between the chiral alcohol sec-phenethyl alcohol and the ester vinylbutyrate Gerrard solubility of hydrogen chloride in solvents Rounaghi and Popov stability constants of sodium complexes with DITHIA-18C6 Lada stability constants of Na and dibenzo-18-crown-6 complex in different solvents Long and Munseon calculated from equilibrium constants for various gaseous proton-transfer reactions with various solvents Abraham solvophobic parameter, calculated from the energies of solute transfer from water to solvents Terradas prochiral selectivity of Pseudomonas sp. lipase in hydrolysis Wescott and Klibanov substrate specificity of the serine protease subtilisin Carlsberg in the transesterification reaction of N-Ac-L-Ser-OEt and N-Ac-L-Phe-OEt with 1-propanol Fletcher absorption of solution Catalań calculated by measuring the difference between the solvation enthalpies of N-methylimidazole and N-methylpyrrole along with SPP scale values Ugo voltammetry determined free energies of proton transfer from water to solvent Treiner experimental single tetraphenylarsenium ion standard free energy of transfer from water to organic solvents Bustamante and Drago experimental values of enthalpies of MIm-solvent system Benoit and Figeys calorimeter-determined enthalpies of solution of 1,8bis(dimethylamino)naphthalene in different solvents Wilhelm and Battino experimental enthalpy of vaporization Sen experimental values of entropy of solvation of electrolyte NaBr Catalań linear combination of the ∆H°solv for the four probes (pyrrole, N-methylpyrrole, benzene, and toluene) Robinson average equilibrium and chromatographic distribution constants on Amberlite XAD-2, SM-2, and XAD-4 Berson endo/exo/ product ratio for the cyclopentadiene-methyl acrylate Diels-Alder addition at 30 °C Maria and Gal enthalpy of complexation of solvents with BF3 in dichloromethane Marcus difference between mean of the Gibbs free energies of transfer of sodium and potassium ions from water to a given solvent and the corresponding quantity for silver ions divided by 100 Kinetic Measurements Bowman and Eisenthal isomerization times of 1,1′-binaphthyl Bowman and Eisenthal reorientation times of 1,1′-binaphthyl Oshima second-order rate constant of the reaction of DDM and TCNE Marcandalli kinetic constants of cis-trans isomerization reaction of 4-nitro-4-diethylaminoazobenzene Kemp and Paul rate constants for decarboxylation of 3-carboxybenzisoxazoles Pyati and Murray electron-transfer rates for the redox couple [Co(bpy)3]2+/3+ Smith first-order rate constant of the ionization of p-methoxyneophyl-p-toluenesulfonate MacFaul measured rate constants for the hydrogen abstraction reactions from aniline by tert-butoxyl radicals Aubry bimolecular rate constants of single oxygen quenching Harano first-order rate constant for rearrangement of o-(1-cyclopropylethyl) S-methyl dithiocarbanate Kevill and Anderson first-rate constants of solvolysis of S-ethyldienzothiophenium Bentley rate constant for solvolysis of CH3OTs in solvent of ionizing power Y relative to rate constant for solvolysis in 80% ethanol Kevill and Anderson specific rates of solvolysis of S-methyldibenzothiophenium ion Pincock rate constants of pyridine-catalyzed decomposition of tert-butylperoxy formate in various solvents at 90 °C Kevill and Anderson first rate constants for the solvolysis of 1-adamantyldimethylsulfonium trifluoromethanesulfonate Takeuchi rate constants of solvolysis of 1-adamantyl tresylate Takeuchi rate constants of solvolysis of 2-adamantyl tresylate Bentley rate constants of solvolysis of 1-adamantyl bromide Bentley rate constants of solvolysis of 1-adamantyl chloride

refsd 130 127 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 30 27

150 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 164 165 165




scalea

no. of solventsb

128 YI 129 YOTf 130 YOTfK

5 8 5

131 χ132 χ+

8 8

133 A 134 a1298 135 Ap

55 26 18

136 BB* 137 Bp

55 18

138 139 140 141 142

28 57 22 84 7

C d DC E Ed

143 Ek

20

144 Em

5

145 Ep

7

146 ES 147 -Es′

14 17

148 J 149 KsLi+

57 10

150 151 152 153 154 155 156 157

Log K Log L16 Log P M N P P′ PKa′

27 168 107 57 57 53 78 8

158 q159 q+ 160 QSi

29 29 7

161 S 162 S′

48 46

163 Vmc 164 XdR

30 52

165 XeR

52

166 XnR

52

167 168 169 170 171 172 173

Xd Xe Xn Y δ ∆ER-P ∆G6Å

72 72 72 42 29 5 25

174 ∆Hacid

36

175 -∆Hf

27 56 23 19 30 29

176 177 178 179

ε0alumina ε0silica εA εB

author(s)c

physical background

Kinetic Measurements (Continued) Bentley rate constants of solvolysis of 1-adamantyl iodide Creary and McDonald first rate constants for solvolysis of 7-norbornyl triflate Kevill and Anderson first rate constants for solvolysis of 2-adamantyl trifluoromethanesulfonate Mitsuhashi calculated from kinetic data of anion solvation Mitsuhasi calculated from kinetic data of cation solvation Other Measurements anion solvating tendency effective hard sphere diameter calculated from data for Gibbs solvation energy for alkali metal cations and halide ions Swain cation solvating tendency Fawcett calculated from data for Gibbs solvation energy for alkali metal cations and halide ions Cilli swelling degree of resin (%) Fowler and Katritzky dielectric constant Khmelnitsky calculated from thermodynamic model of protein denaturation Koppel and Palm acidity derived from ET and P and Y Matyushov and Schmid calculated value for energy of solvent reorganization of density for (bpy)2ClRu(4,4′-bpy)RuCl(bpy)23+ Koppel and Palm derived from Dimroth’s ET polarity parameter by subtracting the contribution of nonspecific solvation Morrone calculated from degree of conversion and ee of the transesterification product Matyushov and Schmid calculated value for energy of solvent reorganization of dipoles for (bpy)2ClRu(4,4′-bpy)RuCl(bpy)23+ Colin eluotropic strength of solvents to different compounds Palm subtract an arbitrary constant 0.25 from the corrected values of Taft’s substituent parameters Fowler and Katritzky expression of dielectric constant Filipek based on polarographic study of Tl-, Li-, Na-, K-, and Cs- complexes with monensin anion Leggett solvatochromic parameter R calculated from other solvent scales Abraham based on logarithmic gas-liquid partition coefficient in n-hexadecane Laane partition coefficient, calculated from hydrophobic fragmental constants Fowler and Katritzky expression of refractive index Fowler and Katritzky dielectric function Koppel and Palm polarizability expression of refractive index Snyder chromatography strength Barrette effective acidity for Brønsted acid-phenol in aprotic solvents by voltammetry test at a platinum electrode Famini and Wilson electrostatic HBAB Famini and Wilson electrostatic HBDA Lauerhaas luminescence quenching ratio of porous Si in solvents to their gasphase dipole moment Brownstein derived from Kosower’s Z values, uses R for process sensitivity Drago solvent polarity, derived from experimental observations ∆χ ) PS′+ W Famini and Wilson molecular volume Rutan selectivity parameter: reflects a composite of solvent dipolaritypolarizability, hydrogen bond basicity, and hydrogen bond acidity Rutan selectivity parameter: reflects a composite of solvent dipolarity and solvent acidity Rutan selectivity parameter: reflects predominately solvent dipolarity, with small contributions from hydrogen bond basicity and acidity Snyder proton donor index Snyder proton acceptor index Snyder strong dipole Koppel and Palm polarity expression of dielectric constant Hildebrand square root of cohesive energy density Jensen and Parker redox potential of perylene Neumann calculated energy necessary to form a cavity of appropriate size for solute of 6 Å diameter from effective hard-sphere diameter of solvent Catalań calculated from enthalpies of solution of two probes, N-methylimidazole and N-methylpyrrole, and relative permittivity Arnett heat of formation for the hydrogen bond Demyanovich and Lynn Park and Carr calculated from other solvent parameters π*, R, and β Park and Carr calculated from other solvent parameters π*, R, and β Famini and Wilson covalent HBDA Famini and Wilson covalent HBAB Swain Wilhelm Fawcett

refsd 166 167 168 169 169 24 170 171 24 171 172 8 173 9 174 77 175 174 176 77 8 177 178 179 180 8 8 9 181 182 183 183 184 185 61 183 186 186 186 181 181 181 9 187 188 189 190 191 192 193 193 183 183


Katritzky et al.


scalea

no. of solventsb

180 181 182 183 184

Θ(∈B) µD πI σ1 γSO2

29 39 30 25 17

author(s)c

physical background

Other Measurements (Continued) Abboud and Taft expression of dielectric constants Abboud and Taft dipole moments Famini and Wilson polarizability index Neumann calculated from surface tension of hard sphere liquid Demyanovich and Lynn experimental infinite dilution activity coefficients of SO2

refsd 194 194 183 189 192

a In alphabetical order for Latin and Greek, respectively. b Some numbers given in this column are arbitrary. Sometimes authors did not number the values, similar measurements were made in different conditions, etc. c Main authors only. d References given in this column are not original references. We tried to choose the references that contained more experimental data. e,f,g To avoid duplication, we renamed B, X, and EB scales to B-2, XX, and EBB, respectively.

Koppel and Palm,17 Kamlet and Taft,18-20 Krygowski and Fawcett,21-23 Swain,24 Mayer,25 Dougherty,26 etc. Empirical properties used to define solvent polarity scales include the following general classes: (i) equilibrium and kinetic rate constants of chemical reactions, (ii) spectroscopic and other properties of solvents, (iii) spectroscopic and other properties of solutes, and (iv) multiparameter approaches.

2.2. Types of Properties Used To Define Solvent Polarity Scales: Division into Major Classes and Definitions The different types of physicochemical properties used to define solvent polarity scales are now considered.

2.2.1. Equilibrium and Kinetic Measurements The influence of solvent on chemical equilibria is determined by the standard molar Gibbs energy of solute (reagent) transfer from one solvent to another or standard molar Gibbs energy of solvation of reagents. Thermodynamically, the standard molar Gibbs energy, ∆G° consists of two components, the enthalpy ∆H° and the entropy term T∆S°, respectively. Consequently, the corresponding enthalpy and entropy functions can be defined also for the solute transfer and solvation. Advances in calorimetry have made standard molar transfer enthalpies readily available. If transfer Gibbs energies and transfer enthalpies are both available, a complete dissection of the effect of the solvents on the various thermodynamic parameters should be possible. The overall solvent effect on a chemical equilibrium constant is determined by the solvation (transfer) free energies of participating reagents and products of the reaction. The contributions from different microscopic interactions (electrostatic, dispersion, hydrogen bonding, etc.) to the transfer free energy of each solute can vary. Therefore, a quantitative description of solvent effects on equilibria proceeding solely from the equilibrium constants of a certain standard reaction would be possible only in simple and favorable cases.3 The same is valid for the use of rate constants and the related free energies of activation of chemical reactions. In each case, apart from the transfer free energies of reagents, the solvation of the transition state of the reaction has to be accounted for. Nevertheless, changes in rate and in equilibrium constants occurring in one reaction series have been

often related to those in another related series. Thus, plotting the logarithms of rate or equilibrium constants for one reaction series against the corresponding constants for a second, related series frequently gives a straight line. Consequently, the linear expression of Gibbs energy relationships in terms of ratios of constants by referring all members of a reaction series to a reference member of the series has been used both in the study of reaction mechanism and in the prediction of reaction rates or equilibrium constants dependent on substituent or solvent changes.3 2.2.1.1. Scales Based on Measurements of Equilibria and Kinetics. A. The µM scale was developed by Marcus27 for determining the “softness” of the solvent. The basic hypotheses and physical meaning concern the standard molar Gibbs energies of transfer ∆tG°(WfS) of ions from a reference solvent (water, W) to other solvents (S). The factor ∆tG°(WfS) should reflect the softness of these solvents in a different manner for hard or soft ions. Other things being equal, especially the charge and size of the ions, hard ions should prefer water and soft ions the softer solvents. Marcus compared the value of ∆tG°(WfS) for Ag+ (considered to be the softest univalent ion) with the mean of ∆tG°(WfS) values for Na+ and K+. Then results form the basis of the softness scale µM, defined as

µM ) {[1/2][∆tG°(Na+, WfS) + ∆tG°(K+, WfS)] - ∆tG°(Ag+, WfS)}/100 (2) The sign of the expression is chosen so as to make µM more positive the softer the solvent S. The division by 100 [for values of ∆tG°(WfS) expressed in kJ/mol] serves to bring the values of µM to a magnitude similar to other solvent property indices used in linear solvation energy relationships, that is, approximately between 0 and 1.27 B. The SP, softness parameter for a solvent S, was defined by Gritzner28 in 1988 on the basis of eq 3:

SP(S) ) 25 + |∆tG°(BCNfS)|

(3)

|∆tG°(BCNfS)| is the absolute value of the standard Gibbs energy change pertaining to the transfer of Ag+ from benzonitrile to solvent S. The addition of 25 kJ/mol and the use of the absolute value of |∆tG°(BCNfS)| are designed to make all values



positive. A study published in 199329 reported additional |∆tG°(BCNfS)| values. The physical meaning of SP is that this parameter is essentially a measure of the interactions between soft acceptor solutes and soft solvents. In principle, the SP scale also contains contributions from a purely electrostatic interaction between Ag+ and the solvent. C. DN and ∆H°BF3. The “donicity number” (DN) was developed in 1966 by Gutmann.10 It is defined operationally as the negative of the standard enthalpy changes, ∆H°SbCl5 for the formation of the 1:1 adduct between antimony pentachloride and an electron pair donor solvent D, both in dilute solution in 1,2-dichloroethane at 25.0 °C and 0.1 MPa:

D (soln) + SbCl5 (soln) T D:SbCl5 (soln)

(4)

∆H°SbCl5 is given by eq 5

∆H°SbCl5 ) ∆H1 - ∆H2

(5)

where ∆H1 and ∆H2 are the enthalpy changes under standard conditions for the following reactions:

D (pure liquid) + SbCl5 (soln) T D:SbCl5 (soln) (6a) and

D (pure liquid) T D (soln)

(6b)

The DN scale has been used particularly in the field of coordination chemistry. Maria and Gal30 have published a very careful critical compilation of the available DN values. Very important also are the results presented by Olofsson and co-workers.31 Maria and Gal30 defined the scale ∆H°BF3 as the standard enthalpy change for the reaction of the formation of the 1:1 adduct between boron trifluoride and electron pair donor solvents D, both in dilute solution in dichloromethane at 25.0 °C and 0.1 MPa:

D (soln) + BF3 (soln) T D:BF3 (soln)

(7)

The ∆H°BF3 values seem to be less affected by the same problems as the DN numbers (reactions of basic impurities, major anomalies for pyridine, triethylamine, hexamethylphosphoric triamide, and HMPA). The basic hypothesis involved in the use of these scales is the assumption that the quantitative ranking of “donicity” they define also holds for the same compounds acting as solvents.

2.2.2. Spectroscopic Measurements Spectroscopic definitions of solvent polarity have been derived from solvent-sensitive standard compounds absorbing radiation in the UV-vis, IR, ESR, and NMR spectral ranges. Theories of solvent effects on absorption spectra assume the isolated and solvated chromophore-containing molecules to be distinct chemical identities and treat these effects simply as a physical perturbation of the relevant molecular states of the chromophores. Onsager’s model of dielectrics32 has been generally used for the theoretical explanation of solvent shifts, even when the theory was derived as a quantum mechanical

treatment, that is, the theory of McRae, which relates solvent-induced frequency shifts to electric dipole interactions.33 According to Reichardt,3 “The term solvatochromism is used to describe the pronounced change in position (and sometimes intensity) of an UV/VIS absorption band, accompanying a change in the polarity of the medium ...”. A hypsochromic (or blue) shift, with increasing solvent polarity, is usually called negative solvatochromism. The corresponding bathochromic (or red) shift is termed positive solvatochromism. The suggestion that solvatochromic dyes should be used as indicators of solvent polarity was first made by Brooker et al.34 in 1951. Bayliss and McRae noticed in 1954 that the solvent effects in electronic absorption spectra are to be expected from (i) the presence of a dipole moment in the solute or solvent molecule, (ii) the change in dipole moment during the optical transition, and (iii) the operation of the Franck-Condon principle.35 They studied solution spectral data for acetone, crotonaldehyde, nitromethane, and nitrobenzene to illustrate these principles.36 Kosower5 in 1958 set up the first comprehensive solvent scale. The most important solvent polarity scales developed using empirical parameters from spectroscopic measurements include the following. 2.2.2.1. “Solvation” Scales Derived from Spectroscopic Measurements. A. ET(30) and ETN 3 are defined as the molar transition energy, in kcal/mol, for the long wavelength electronic transition of a 2,6diphenyl-4-(2,4,6-triphenylpyridinio)phenolate dye (Dimroth-Reichardt’s betaine dye) as a solution in the solvent under investigation at 25 °C and at a pressure of 0.1 MPa. The ET(30) values are obtained from the experimentally determined wavelength of the absorption maximum of this transition (λmax) through eq 8:

ET(30)/(kcal/mol) ) 28591/(λmax/nm)

(8)

ETN is a dimensionless “normalized” scale, defined by eq 9, wherein tetramethylsilane (TMS) and water are selected as the “polarity” extreme cases.

ETN (solvent) ) [ET(solvent) - ET(TMS)]/ [ET(water) - ET(TMS)] (9) B. Z 37 is based on the high solvent-sensitivity of the frequency of the charge-transfer absorption band of the indicator 1-ethyl-4-methoxycarbonylpyridinium iodide. Kosower defined his polarity parameter for a given solvent as the molar transition energy, in kcal/ mol, for the long-wavelength electronic transition of 1-ethyl-4-methoxycarbonylpyridinium iodide, dissolved in the solvent under consideration at 25 °C and at a pressure of 0.1 MPa. Values of Z are obtained through an expression similar to eq 8, from the experimentally determined wavelength of the absorption maximum of this transition (λmax). C. Zt 14 is the symbol proposed by Marcus to be used for the scale of medium effects based on the solvatochromic shifts undergone by the longest wavelength band in the electronic absorption spectrum of


Katritzky et al.

4-cyano-1-ethylpyridinium iodide. Medium effects on the corresponding transition energies are linearly related to Z values to a very high degree of correlation and a standard deviation of 0.5 kcal/mol. D. The Ds scale was defined by Persson, Sandstro¨m, and Goggin38 in 1986, based on the shifts undergone by the position of the symmetric Hg-Br stretching vibration in mercuric dibromide, HgBr2, on going from the gas phase to the solvent (eq 10). The σ values were determined at 25.0 °C by Raman spectroscopy; the uncertainties in σ are estimated as =1 cm-1.38

Ds ) σHg-Br(gas) - σHg-Br(solvent)

(10)

E. G is the scale developed by Schleyer and Allerhand39 on the basis of a quantitative study of the solvent shifts undergone by the positions of the stretching vibrations, σ, of selected X ) O oscillators. The authors defined the G scale through eq 11, wherein σO and σS, respectively, stand for the positions of the stretching vibration of X ) O in the gas phase and in solvent S, and a is a constant characteristic of the probe. In the development of the scale, these authors used the carbonyl stretching bands of N,N-dimethylformamide and benzophenone40 and the SO stretch of DMSO.41 In 1986, Somolinos, Garcıá, and others42 revised and extended the G scale, also at 0.1 MPa and “room temperature”.

aG ) (σO - σS)/σO Luç on43

(11)

Later, Nicolet, Laurence, and studied in 1987 the solvent shifts undergone by the CdO stretching band of methyl trichloroacetate. It became obvious that this band has several features that make it particularly suitable as a molecular probe. Finally, Kolling measured the position of the carbonyl stretching vibration of ethyl acetate44 and butanone45 in a variety of solvents at 298.15 K and 0.1 MPa. 2.2.2.2. Scales of Dipolarity/Polarizability Based on Spectroscopic Measurements. The basic concept of these scales is that the solute-solvent interactions can be dissected into “general”swhich have electrostatic and dispersive origins and can be related conceptually to reaction field theoriessand “specific” interactionsswhich include hydrogen-bonding and/or donor-acceptor interactions.3 A. π* was defined by Kamlet, Abboud, and Taft18 and intended to provide a quantitative measure of the nonspecific part of van der Waals interactions between solvents and solutes. The scale was based on the treatment of the solvatochromic shifts undergone by selected absorption bands of a variety of aromatic molecules (“molecular probes”). Given a solvatochromic indicator, the π* value for a solvent S was defined through eq 12. σ(S) pertains to the frequencies of the maximum of the solvatochromic band in the various solvents. Cyclohexane (c-C6H12) and dimethyl sulfoxide (DMSO) were used as references by defining π*(c-C6H12) ) 0 and π*(DMSO) ) 1.

π* (S) ) [σ(S) - σ(c-C6H12)]/ [σ(DMSO) - σ(c-C6H12)] (12) In 1986, Laurence and Nicolet,46 after careful examination of the original conditions (temperature, medium effects, etc.) used for the construction of the π* scale, concluded that (i) the solvatochromic band of the most used indicator, p-(diethylamino)nitrobenzene, has significant vibrational structure, leading to a solvent-dependent band shape; (ii) π* values are somewhat solute-dependent; and (iii) for a given indicator, π* values are temperature-dependent (“thermosolvatochromism”). M. T. Dalati47 reported in 1991 the frequencies of the solvatochromic bands of p-methoxynitrobenzene and p-(dimethylamino)nitrobenzene in 276 solvents at 25.0 °C and 0.1 MPa. The corresponding π* values were obtained for each of these two indicators (π*NMe2 and π*OMe) by means of eq 12 and the conditions π*(cC6H12) ) 0 and π*(DMSO) ) 1. An analysis of these π*, π*NMe2, and π*OMe values demonstrated that they are generally interrelated but can show significant quantitative differences. B. SPP (solvent polarity-polarizability), reported by Catalań et al.,48 is based on the solvatochromic shifts undergone by the long-wavelength absorption maximum of two indicators: 2-(dimethylamino)-7-nitrofluorene (DMANF) and 2-fluoro-7-nitrofluorene (FNF). For a given solvent S, the value of this parameter is defined through eq 13:

SPP (S) ) [∆σ(S) - ∆σ(c-C6H12)]/ [∆σ(DMSO) - ∆σ(c-C6H12)] (13) Catalań et al.48 proposed a scale with a different normalization (SPPN) wherein the origin is not ∆σ(c-C6H12) but rather the calculated value of ∆σ(gas). C. π*azo scales based on the solvatochromic shifts undergone by the longest wavelength absorption band (nfp* and πfp* transitions) of a set of six azo merocyanine dyes were reported by Buncel and Rajagopal.49 Studies were made of the spectra of the six indicators in 29 different solvents (25 of which were either non-hydrogen-bond donors or weakhydrogen-bond donors). The frequencies of the maxima were determined at 25 °C and under 0.1 MPa. Buncel and Rajagopal could thus demonstrate that the qualities of the correlations of medium effects on solute properties obtained using π* or π*azo are very close, indicating that these scales all keep only little “model-dependent” specificity.50 D. π*2 is a scale developed by Abe51 based on the solvatochromic shifts undergone by the long-wavelength electronic absorption transitions of three indicators: naphthalene, anthracene, and β-carotene. The scale was normalized by taking π*2 ) 0 for the gas phase and π*2 ) 1 for c-C6H12 solvent. For any given solvent S, π*2 (S) was given by eq 14. Abe observed that solvent effects on the frequency of the electronic transition of anthracene are linearly related to a high degree of precision. This correlation was used to generate π*2 values for solvents for which no naphthalene data were available.



π*2 (S) ) [σ(S) - σ(gas)]/[σ(c-C6H12) - σ(gas)] (14) 2.2.2.3. Basicity Scales. These scales quantify the “specific” solute-solvent interactions in which the solute plays the role of an electron pair acceptor and the solvent, an electron pair donor. Here we discuss only some frequently used scales of hydrogen bonding and basicities of solvents. A. ∆νOD (∆σOD) and B Scale. In 1940, Stanford and Gordy52 used the sensitivity of the O-H (or O-D) oscillators to hydrogen bonding as a tool to quantify the Lewis basicity of molecules. Kagiya, Sumida, and Inoue53 determined the positions (cm-1) of the O-D stretching band of monomeric methanol [2H] in different solvents and took the difference between the positions of the absorption maximum in solvent S and in benzene, ∆σOD ) σ(S) - σ(C6H6), as a quantitative measure of the HBA character of these solvents. In 1976, Burden, Collier, and Shorter54 revised and extended this study. Koppel and Palm9 defined a scale of Lewis basicity of solvents, B, through eq 15, wherein σOD(gas) and σOD(S) stand for the values of σOD in the gas phase and in solvent S.

B ) σOD(gas) - σOD(S)

(15)

B. The B′ scale was developed by Koppel and Paju55 by redefining the scale B of solvent Lewis basicity through eq 16

B′ ) ∆σPhOHCCl4 ) σPhOHCCl4 - σPhOH-SCCl4

(16)

wherein σPhOHCCl4 stands for the position (in cm-1) of the O-H stretching mode of monomeric phenol in tetrachloromethane solution and σPhOH-SCCl4 is the position of the O-H stretching mode of phenol within the 1:1 complex with molecule S in tetrachloromethane solution. According to Koppel and Paju,55 “... the representation of the solvent basicity parameters by eq 16 is equivalent to the introduction of the postulate that base-induced shifts of the stretching frequencies of the X-H band of the donors in infinite dilution in inert media can also characterize the Lewis basicity of the corresponding pure bases as solvents”. C. β scales are based on the concept of the “solvatochromic comparison method” set forth by Kamlet and Taft.19 The first fundamental assumption of the solvatochromic comparison method is that the same linear relationship holds for the nonspecific part of the solvent effect in the presence of hydrogen bonding. The second is that this contribution is proportional to the value of the π* parameter for the solvent S under scrutiny. From the positions of the solvatochromic bands of the hydrogen-bonding donor indicator i, and its homomorph j in solvent S, respectively σS(i) and σS(j), it was found that eq 17 holds for non-hydrogenbonding solvents:

σS(i) ) aijσS(j) + bij

(17)

The experimental value of σS(i) for a hydrogenbonding acceptor solvent is significantly different

from the predicted value obtained by using eq 17. The difference, ∆σS(i) ) [σS(i)]exptl - [σS(i)]pred, has been used to “measure” the hydrogen-bonding acceptor character of the solvent. Initially, the compound pairs 4-nitrophenol/p-methoxynitrobenzene and 4-nitroaniline/p-(diethylamino)nitrobenzene were used as indicators. The β scale of hydrogen-bonding basicity was constructed on the basis of the scaled ∆σS(i) values determined for these indicators (β ) 0 for c-C6H12 and β ) 1 for HMPA) and showed that these “solvatochromic betas” correlate to a high degree of precision with the logarithms of the equilibrium constants for the 1:1 hydrogen-bonding associations between 4-fluorophenol or phenol and a large number of bases in CCl4 solution.19 Laurence, Nicolet, and Helbert,56 in a study of solvatochromic indicators, showed that p-(dimethylamino)nitrobenzene is a better indicator than p(diethylamino)nitrobenzene. Furthermore, they were able to compare the homomorphic couples 4-nitrophenol/4-methoxynitrobenzene and 4-nitroaniline/4(dimethylamino)nitrobenzene in a series of studies performed on purified and dried solvents at 25.0 °C and 0.1 MPa. They confirmed that in the absence of hydrogen-bonding interactions, the linear relationship between the positions of the homomorphic indicators holds to an extremely high degree of precision. Abboud and Notario,16 by strictly applying the solvatochromic comparison method to each of these homomorphic couples, determined and compared the β values for all of the solvents for which data were available. They presented their results as βOH (4nitrophenol/4-methoxynitrobenzene) and βNH2 (4nitroaniline/4-(dimethylamino)nitrobenzene) values. This comparison showed that, although the hydrogenbonding acceptor rankings defined by these parameters are roughly similar, the linear relationship between βOH and βNH2 is solvent family dependent. D. The SB scale was developed by Catalań et al. in 199657 by applying the solvatochromic comparison method to the pair of homomorphs 5-nitroindoline and 1-methyl-5-nitroindoline. The authors used the difference between the positions of the longest wavelength absorption band of these homomorphs in the UV-vis region as a quantitative measure of the hydrogen-bonding acceptor character of the solvent. The value of the normalized parameter SB (“solvent basicity”) for any given solvent is defined through eq 18, wherein ∆σ (gas phase) was obtained by extrapolation of the ∆σ values for n-alkanes and TMG (tetramethylguanidine). TMG leads to the largest hydrogen-bonding basicity effects in their study. Catalań et al.57 observed that (with the single exception of pyridine), SB and βOH correlate to a satisfactory degree of precision.

SB ) [∆σ (solvent) - ∆σ (gas phase)]/ [∆σ (TMG) - ∆σ (gas phase)] (18) E. The σCO and ∆σCO scales are based on a study published in 1987 by Nicolet, Laurence, and Luç on43 on the solvent shifts undergone by the CdO stretching band of methyl trichloroacetate (CCl3COOMe) and trichloroacetic acid (CCl3COOH). The authors


Katritzky et al.

applied the “IR comparison method” to the abovementioned pair. The basic concepts of this method are as follows: (i) for solvents that are not or only extremely weak hydrogen-bonding acceptors and for the gas phase, the positions of the CdO stretching bands of both compounds are linearly related to a high degree of precision, and (ii) the hydrogenbonding basicity of a hydrogen-bonding acceptor solvent is given by the difference between the experimental value of σ(CCl3COOH) and the value calculated by means of eq 18.

2.2.3. Multiparameter Approaches Katritzky et al.8 tested various multiparameter equations using linear combinations of existing empirical solvent parameters. They combined successfully ET values with functions of the dielectric constant and index of refraction. Using ET and the Kirkwood function (r - 1)/(2r + 1), a two-parameter equation was constructed that allows independent variation of dipole/dipole and hydrogen-bonding forces. This equation is based on the assumptions that the Kirkwood function adequately represents dipole/ dipole interactions and that ET values are sensitive to both dipolar interactions and the interaction between solute and hydrogen-bond donor solvents. Koppel and Palm9,58 used eqs 19-24 to define four parameters for characterizing solvents: polarity (Y), polarizability (P), electrophilicity/acidity (E), and nucleophilicity/basicity (B). In the following, the functions ( - 1)/(2 + 1) or ( - 1)/( + 2) are denoted by Y (“polarity”) (eqs 19a and 19b), and the function (n2 - 1)/(n2 + 2) is denoted by P (“polarizability”) (eq 20).

Y ) ( - 1)/(2 + 1)

(19a)

Y ) ( - 1)/( + 2)

(19b)

P ) (n2 - 1)/(n2 + 2)

(20)

or

The authors found that a rather satisfactory linear relationship exists between functions ( - 1)/(2 + 1) and ( - 1)/( + 2).9 According to Koppel and Palm, in practice the choice between these different formally equivalent dielectric functions is arbitrary and depends more on scientific traditions of the general application of these functions in physics and chemistry and on personal preference. Equation 19a, as function of , and eq 20, as function of n, were preferred for correlations of the contributions of nonspecific solvation to solvent effects on ∆ν (IR spectra), log(solubility) values, etc. In their treatment of solvatochromic shifts in electronic spectra, eqs 19b and 20 were used. Using these two parameters, Y and P, the authors have performed a least-squares regression analysis of the chemical and spectroscopic data according to eq 21, where A is the solvent-sensitive characteristic for a given process, Y and P are the above-defined functions of and n, and A0, y, and p are the regression coefficients. According to its physical meaning A0 is equal to the A value, for the gas phase

( ) n ) 1 for a vacuum, and Y ) P ) 0), and y and p represent the susceptibilities of the process to the influences of solvent polarity and polarizability, respectively.

A ) A0 + yY + pP

(21)

Consequently, subtraction of the corresponding polarity (yY) and polarizability (pP) contributions from the total solvent effect has led the authors to the definition of a contribution, ∆Asp, from specific solvent-solute interactions, eq 22.

∆Asp ) A - A0 - yY - pP

(22)

According to eq 22 the electrophilic solvation power, E, of the solvent has been defined by eq 23, where ET is Dimroth’s solvent polarity parameter, based on the solvent-dependent electronic πfπ* transitions for N-phenolpyridinium betaines.

E ) ET - 25.57 - 14.39Y - 9.08P

(23)

The fourth parameter developed by Koppel and Palm, nucleophilicity/basicity (B), has been discussed before (see section 2.2.2.3.A, eq 15). They used these four parameters to build one of the best known of the multiparameter solvent scales or linear free energy relationships (LSER). The multiparameter equation describing both the nonspecific (Y, P) and specific (E, B) components of solvent-solute interactions sometimes also contains the isosteric effect of solvent molecules (eq 24), where e and b characterize the sensitivity of a given process toward electrophilic and nucleophilic solvation effects, respectively. The conditions e ) 1 and b ) 1 hold for the reference processes, that is, the πfπ* transitions for N-phenolpyridinium betaine and IR stretching frequency shifts of CH3OD, respectively. The equation has been applied to the description of some 60 solvent-dependent properties with good results.9

A ) A0 + yY + pP + eE + bB

(24)

An empirical two-parameter approach for the description of solvent effects has been proposed by Krygowski and Fawcett.21 Considering that only specific solute/solvent interactions need to be considered, the authors postulated that the solvent effect on a solute property A can be represented as a linear function of only two independent but complementary parameters describing the Lewis acidity and Lewis basicity of a given solvent. These parameters were chosen to be the ET values (as a measure of Lewis acidity) and Gutmann’s donor numbers (DN) (as a measure of solvent basicity) (eq 25), wherein R and β are regression coefficients describing the sensitivity of the solute property A to electrophilic and nucleophilic solvent properties, respectively. The regression coefficients were normalized.

A ) A0 + RET + β(DN)

(25)

Swain et al.24 have also given a two-parameter treatment of solvent effects. According to their study



all solvent effects can be rationalized in terms of two complementary solvent property scales, one measuring the solvent’s anion-solvating tendency or “acity” (Aj) and another measuring the solvent’s cationsolvating tendency or “basity” (Bj) (eq 26). Aj and Bj characterize the solvent j; A and A0 as well as the multiple regression coefficients ai and bi depend only on the solvent-sensitive solute property i under study. Constants ai and bi represent the sensitivity of solute property i to a solvent change. The authors used a nonlinear least-squares procedure to evaluate and optimize all constants for 1080 data sets in order to get the best possible fit consistent with eq 26.

A ) A0 + aiAj + biBj

(26)

Mayer25 introduced a semiempirical multiparameter relationship, eqs 27a and 27b, for the description of solvent effects on the thermodynamics and kinetics of chemical reactions, wherein ∆G represents the Gibbs energy of reaction or activation (∆G#), DN the donor number, AN the acceptor number,59 and ∆Gvp0 the standard molar Gibbs energy of vaporization of a solvent S and a reference solvent R, respectively. Acetonitrile was used as a reference solvent (∆Gvp0 ) 5.31 kJ/mol).25

∆GS - ∆GR ) a(DNS - DNR) + b(ANS - ANR) + c(∆Gvp0S - ∆vp0R) (27a) ∆∆G ) a[∆(DN)] + b[∆(AN)] + c[∆∆Gvp0] (27b) Dougherty26 developed a multiparameter correlation by considering the interaction between the highest occupied orbitals (HOMO) of the solvent and the ions and the corresponding lowest unoccupied orbitals (LUMO) of the ions and the solvent. The energies of these orbitals were approximated from ionization potentials and electron affinity data. Another multiparameter equation for the correlation of solvent effects on physicochemical properties has been proposed by Drago:60,61

∆χ ) W + E*AEB + C*ACB + PS′

(28)

where S′ is the “universal” descriptor of solvent polarity according to Drago, P is a solute parameter intended to measure the susceptibility of the solute probe to polarity, and W is a nonzero intercept at S′ ) 0. With the E*AEB and C*ACB terms, eq 28 includes the well-known E/C equation of Drago that describes the specific EPD/EPA interactions between a Lewis acid A and a Lewis base B. The acid A and the base B are both characterized by two empirical parameters, E and C, and it is assumed that the standard enthalpy of a 1:1 Lewis acid/base interaction can be divided into two terms, E*AEB and C*ACB, which are said to correspond to the strength of electrostatic and covalent contributions in the acid/base interactions, respectively.62 2.2.3.1. Linear Solvation Energy Relationships (LSER). Linear Gibbs energy relationships are known as “extrathermodynamic” combinations of detailed models with thermodynamic concepts. This

approach to model building lacks the rigor of thermodynamics, but it can provide information not otherwise accessible. Although linear Gibbs energy relationships are not a necessary consequence of thermodynamics, their wide occurrence suggests that the nature of this connection between the correlated quantities can usefully be explored.3 The functional relationships between substituent or solvent parameters and various substituent- or solvent-dependent processes take the form of linear Gibbs energy relationships, frequently still known as linear free energy relationships (LFER). One of the best-known LFERs is the Koppel-Palm multiparameter equation described in the previous section. Taft et al.63 introduced the term linear solvation energy relationships for generalized treatment of solvation effects, which assumes that attractive solute-solvent interactions are frequently of two kinds: (i) nonspecific dipolarity/polarizability64 and (ii) specific hydrogen-bond complex formation.19 Class ii is subdivided into solute hydrogen-bond donor (HBD)/solvent hydrogen-bond acceptor (HBA) complexing and (the converse) solute HBA/solvent HBD complexing. LSER further assume linear free energy or electronic energy relationships for each of the contributing terms to the observed solvent effects. The potential relevance of each contribution is judged by knowledge and theoretical concepts of effects of the molecular structure on solutes and solvents and the nature of the measured property. The defining measured properties are molecular properties (e.g., dipole moments), spectroscopic solvent shifts, or molecular affinities, which are measured by formation constants. The “solvatochromic parameters” describing solute and solvent properties, which have been widely used by Kamlet, Abboud, Abraham, and Taft in their studies,19,20,63 comprise the following terms. π*, a measure of solute or solvent dipolarity/ polarizability, estimates the ability of the solvent to stabilize a charge or a dipole by virtue of its dielectric effect. For “select solvents” (i.e., nonprotonic aliphatic solvents with a single dominant bond dipole), π* values are proportional to the dipole moment of the solvent molecule.65 The π* scale was selected to run from 0.0 for cyclohexane to 1.0 for dimethyl sulfoxide. δ, a discontinuous “polarizability correction term”, is equal to 0.0 for non-chlorine-substituted aliphatic solvents, 0.5 for poly-chlorine-substituted aliphatics, and 1.0 for aromatic solvents. δ values reflect the observation that differences in solvent polarizability are significantly greater among the three solvent classes than within the individual classes.66 R, a scale of HBD acidities, applies to self-associating compounds when they act as solvents. R describes the ability of a solvent to donate a proton in a solventto-solute hydrogen bond. The R scale was selected to extend from 0.0 for non-hydrogen-bond donor solvents to ∼1.0 for methanol. Rm applies to self-associating compounds when they are acting as “monomeric” solutes. β, a scale of HBA basicities, applies to self-associating compounds when they act as solvents. β describes


the solvent’s ability to accept a proton or donate an electron pair in a solute-to-solvent hydrogen bond. The β scale was selected to extend from 0.0 for nonhydrogen-bond donor solvents to ∼1.0 for hexamethylphosphoric acid triamide (HMPT). βm applies to self-associating compounds when they are acting as “monomeric” solutes. ω, an amphiprotic hydrogen-bonding parameter, is used for amphiprotic compounds in aqueous solution in place of β. For unsubstituted alkanols, ω = βm. δH is the Hildebrand solubility parameter; δH2 measures the solvent’s contribution to the cavity term and corresponds to the cohesive pressure c, which characterizes the energy associated with the intermolecular solvent/solvent interactions. Thus, δH2 is considered as a measure of the enthalpy or Gibbs energy input required to separate solvent molecules to provide a suitably sized cavity for the solute. V, the solute molar volume, is usually defined as the molecular weight divided by the liquid density at 25 °C. V measures the solute’s contribution to the cavity term. The authors67 used V/100 so that the cavity parameter covered roughly the same range as the dipolarity/polarizability and hydrogen-bonding parameters, which makes easier the evaluation of the contributions of the three types of effects to the solubility property studied. ξ is a coordinate covalency parameter used to correlate certain types of so-called family-dependent solute basicity properties.20,68 The ξ values are interpreted as being approximate measures of the relative coordinate covalencies of the bonds that are formed between solute and solvent at the base center of the solvent. Coordinate covalencies of solute/solvent adducts of a given solute acid decrease in strength (ξ decreases) as the electronegativity of the solvent base center increases, because the positive charge created by coordinate covalency on an increasingly electronegative atom is unfavorable; ξ reconciles the β scale with the pKa scale.

XYZ ) XYZ0 + cavity term + dipolar term + hydrogen-bonding term (29) A large number of solubility and solvent-dependent properties,69 XYZ, depend on three terms as shown in eq 29. Here the cavity term measures the free energy or enthalpy input required to separate the solvent molecules to create a suitably sized cavity for the solute. The dipolar term measures the exoergic effects of solute/solvent dipole-dipole, dipole-induced dipole, and mutually induced dipole interactions. The hydrogen-bonding term measures the exoergic effects of hydrogen-bonding (or Lewis acid/base) complexation between the solute and the solvent. Equation 29 with solvatochromic parameters appropriately included becomes eq 29a, where the subscript 1 is applied to the solvent and subscript 2 to the solute.

XYZ ) XYZ0 + A(δH2)1V2/100 + Bπ*1π*2 + CR1(βm)2 + Dβ1(Rm)2 (29a)

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When the effects of multiple solvents on a single solute or set of reactants are involved, correlations are expressed in terms of the solvatochromic parameters of the solvents (eq 29b).

XYZ ) XYZ0 + h(δH2)1 + sπ*1 + aR1 + bβ1 (29b) When the solubility properties of multiple solutes in single solvents or distributions between pairs of solvents are involved, the correlations are expressed in terms of the solvatochromic parameters of the solutes (eq 29c).

XYZ ) XYZ0 + mV2/100 + sπ*2 + bβ(or βm or ω)2 + aR(or Rm)2 (29c) When aromatic and aliphatic solutes or solvents are included in the same correlation, the δ parameter often needs to be used in conjunction with π*.66 For certain types of “family-dependent” basicity properties,20,63 the ξ parameter needs to be used in conjunction with β. XYZ properties analyzed by Kamlet and Taft have included solubilities of various type solutes in chemical solvents and biological tissues and fluids and free energies of solution and of transfer between solvents among the diverse properties, which have been correlated. This work has been documented in an impressive series of more than 40 articles titled “Linear Solvation Energy Relationships” and has appeared: Part 170 ... Part 44.71 Abraham and co-workers72 performed an analysis of solute hydrogen-bond basicity in terms of complexation constants (log K) using F1 and F2 factors, the principal components of different kinds of basicity. The authors used two constants, S1 and S2, to define an angle θ as a measure of the electrostatic covalent bonding ratio in the hydrogen-bond complex. Abraham observed that among a wide range of reference acid/solvent systems, θ varies only from 64 to 73°, and he suggested that a reasonably general scale could be set up for bases using these reference systems. Additionally, Abraham et al.73 set up two scales of solvent hydrogen-bond basicity: (i) β1 (general), constructed using the solvatochromic indicator method and a series of double-regression equations (for 11 aniline-type indicators), and (ii) β1 (special), constructed by the homomorphic comparison method using only 4-nitroaniline and 4-nitro-N,N-dimethylaniline as indicators. The authors showed that although there is a general connection between these two solvent hydrogen-bond basicity scales and the socalled solute scale, β2 (pKHB), obtained from log K values for hydrogen-bond complexation of bases with 4-fluorophenol in CCl4, the use of β1 to predict β2 and vice versa is a very hazardous procedure. By using the β2H scale of solute hydrogen-bond basicity, formulated from 1:1 hydrogen-bond complexation constants in CCl4, Abraham74 formulated a scale of effective or summation hydrogen-bond



basicity. The method used by the author is based on eq 30, where SP is a set of solute water-solvent

log SP ) C + rR2 + sπ2H + aΣR2H + bΣβ2 + vVx (30) partition coefficients in a given system, R2 is an excess molar refraction, π2H is the solute dipolarity/ polarizability, ΣR2H and Σβ2 are the effective solute hydrogen-bond acidity and basicity, and Vx is McGowan’s characteristic volume. 2.2.3.2. Statistical Scales. Statistical scales are in principle “model-independent”. They are constructed by statistically averaging medium effects on the physical properties or reactivity data of a wide number of solutes. The choices of the solutes and/or properties represent potential limitations of these scales. A and B scales were defined in 1983 by Swain et al.,24 who analyzed 1080 data for 61 solvents and 77 reactions according to the bilinear model described by eq 31, wherein P(S) is the value taken by property

P(S) ) aA(S) + bB(S) + c

(31)

P in solvent S; a, b, and c are constants depending only on the solute and the property under consideration. A and B are, respectively, the anion-solvating (“acity”) and the cation-solvating (“basity”) tendencies of S. The A and B values were determined from statistical study of the database indicated above together with boundary conditions: A ) B ) 0 for n-heptane, A ) B ) 1 for water, A ) 0 for HMPA, and B ) 0 for trifluoroacetic acid. Both non-hydrogenbond donors and hydrogen-bond donors were involved in this study. Analysis of these two scales shows that they both fail to comply with the mathematical condition of orthogonality that should have been imposed, and neither conveys accurately the putative physical meaning intended.16 B. S′ was introduced by Drago in 199260 and is based on the statistical treatment of 30 molecular probes and 31 solvents. The data were analyzed on the basis of the correlation of eq 32, wherein ∆χ

∆χ ) S′P + W

(32)

stands for the effect of the solvent on the physicochemical property under consideration, S′ is the “universal” descriptor of solvent polarity conforming with Drago, P is a solute parameter intended to measure the susceptibility of the solute probe to polarity, and W is a nonzero intercept at S′ ) 0.

2.3. Detailed List of Solvent Scales with References and Number of Solvents Table 1 presents a detailed list of solvent scales collected from the literature,8,9,14,24,27,30,38,39,47-49,51,53,55, 57,61,62,75-194 together with the number of solvents involved in the development of every scale, the physical background, and main authors. Analysis of the data in Table 1 demonstrates that 44% of the scales are developed using spectroscopic measurements, 15% use equilibrium, and 13% use kinetic measurements, and those based on other

methods represent 28% from a total of 184 classified solvent scales. The number of solvents used for developing a solvent scale has varied from 5 to >100. Understandably, the larger data sets were used for spectroscopic measurements and the smaller ones for equilibrium (except Gutmann’s scale, DN) and kinetic measurements. Consequently, existing solvent scales based upon spectroscopic measurements are more commonly used than others. A disadvantage of most of the scales of Table 1 is that in addition to nonspecific effects, they contain specific effects, which are unique to the probe (solute) used to develop each scale. As a result, each scale differs for reasons that are not obvious, and this inhibits the understanding of solvent influence on new solutes. Moreover, many of the scales presented above are limited to a specific range of solvent polarity or other property due to restrictions in the methodology of their measurements: for instance, the probe compound can become insoluble or unstable under some conditions. This means that any individual solvent is rarely represented in all common scales and no scale covers all common solvents. There are other criteria describing the quality of an individual solvent scale besides the number and range of solvents it holds or the limitations on the expansion introduced by the probe itself. For instance, spectroscopic scales can be compared according to the solvatochromic range (sensitivity to polarity change of the absorption band under investigation) of their respective probes. Obviously, the larger the shift of the band, the higher can be the possible accuracy/sensitivity of the scale derived from this shift. A number of probe molecules together with their solvatochromic range have been compiled by Reichardt.62 The ET(30) scale is representative of a scale based on probes with an outstandingly high solvatochromic range (-9730 cm-1), some 5 times larger than the range of the probe of Φ (-1865 cm-1). The necessary concentration of the probe molecules for the measurement may serve as another parameter for the comparison of scales. If the absorption bands can be produced only in relatively high concentrations, interaction and even aggregation of the probes may occur, making assumptions of pure solvent polarity dependence questionable. The concentration problems are also often common to scales based on NMR measurements. The solubility of the probes often sets limits on the range of solvents in a scale; a common practice is to use (an) additional probe(s) with better solubility for the extension of the scale. The loss of accuracy comes from the fact that the correlation between the transitions energies of the probes used is seldom perfect; unfortunately, all of the values of a scale are commonly assigned the same precision. The same is often true for scale values that are measured at some other temperature. Although some model processes are independent of temperature, some others have strong dependencies, and the corresponding scale values should not be attributed the same precision as others.


Several scales were introduced a long time ago. Experimental techniques for the measurements involved in some of them have improved considerably (i.e., IR spectroscopy measurements for the G scale, calorimetry for DN). It would now be possible to remeasure the values for these scales and, thus, improve their accuracy. The last but not least criterion is the general clarity of the model process. It is rather important to understand which types of interactions are present between the solvent and the probe. A good model process should involve predominantly the same type of interactions over the whole range of solvents. Over the years, overall progress in chemical understanding, including the development of quantum chemistry, has considerably reduced uncertainties of the possible types of interaction as has been illustrated for the case of basicity scales.195

2.4. Attempts To Relate Scales to Descriptors A main objective of solvent polarity scales is to facilitate the systematic correlation and analysis of chemical and physicochemical properties in solution. The macroscopic (bulk) properties of chemical compounds clearly depend on their microscopic (structural) characteristics. It has not been possible to define solvent polarity in terms of macroscopic solvent properties, and as a result many empirical solvent polarity scales have evolved as an alternative approach for predicting or analyzing solvent effects (see Table 1). The ability to calculate free energy changes associated with solvation allows calculation of differential free energies in solution without having to model complex changes in hydrogen-bonding networks, conformational changes, or other differential solvation issues for which there is little direct information.196 Recently, significant effort has been directed in trying to model and relate complex solvent effects to solvent scales using fundamental molecular properties or descriptors: both empirical and theoretical. The LSER descriptors based on LFER are demonstrated to be successful in correlating a wide range of chemical and physical properties involving solutesolvent interactions of compounds.65,197 The coefficients of the descriptors in the correlation equations are expected to provide insight into the physical nature of the solute-solvent interactions related to the experimentally observed phenomena or data. The original LSER descriptors (also called the solvatochromic descriptors) were derived from UV-vis spectral shifts of indicator dyes. Thus, their ability to make a priori predictions has been somewhat limited because of their empirical origin. Although there exist tables of LSER parameters and predictive relationships to help in their estimation, LSER descriptors for new compounds are not easily defined. Attempts to correlate computationally derived structural and electronic descriptors with the solvatochromic parameters have met with only moderate success.198 In 1987, on the basis of two distinct studies, Abraham et al. showed that (i) solvolysis/dehydrohalogenation rates of (CH3)3CCl in 21 HBD and non-

Katritzky et al.

HBD solvents are correlated by an LFER in terms of δH2 (solvent cohesive energy) and π, R, and β (the solvatochromic parameters that scale solvent dipolarity-polarizability, hydrogen-bond-donor acidity, and hydrogen-bond-acceptor basicity);199 (ii) at least four solvent parameters are needed in any general equation to model solvent effects on rate constants or on Gibbs energies of individual solutes: as parameters in the general equation they used π* (the solvent dipolarity), R (the solvent hydrogen-bond acidity), β (the solvent hydrogen-bond basicity), and δH2 (the solvent cohesive energy).200 In an approach to circumvent problems associated with the LSER parameters, Famini and co-workers developed a new set of computationally derived descriptors, called “theoretical LSER” (TLSER).201,202 The TLSER attempts to maintain the same relationship between property and parameters; that is, it incorporates steric, polarizability, and hydrogenbonding terms. However, each TLSER term is derived by a semiempirical molecular orbital method, permitting a much greater degree of a priori prediction once a correlation is derived than does LSER. Like LSER, TLSER uses a single set of descriptors (six for the TLSER) and each parameter describes a single, orthogonal molecular event of characteristics.

log(γ) ) c0 + c1Vmc + c2π* + c3a + c4b + c5q+ + c6q- (33) The most general form of TLSER is expressed in eq 33,202 where Vmc is the molecular van der Waals volume calculated according to the method of Hopfinger.203 The polarizability term π* is derived from the polarization volume computed by using the method of Kurtz.204 The hydrogen-bonding effects are separated into donor and acceptor components. The covalent contribution to Lewis basicity, b, is represented as the difference in energy between the lowest unoccupied molecular orbital (LUMO) of water and the highest occupied molecular orbital (HOMO) of the solute. The electrostatic basicity contribution, denoted q-, is simply the most negative atomic charge in the solute molecules. Analogously, the hydrogenbonding donating ability is divided into two components: a is the energy difference between the HOMO of water and LUMO of the solute, whereas q+ is the most positive charge of a hydrogen atom in the solute molecule. The advantage of using this single set of descriptors has been demonstrated in the ability to compare disparate properties and data set. An implicit assumption of the TLSER approach is that the descriptors are “pure” and reflect a particular microscopic property without “mixing” or contamination from other descriptors. Although it is impossible to prove it in a “global” sense, most of the TLSER regressions to date have very small crosscorrelations among descriptors. Engberts et al.205 correlated the effect of 30 solvents on the CdO stretching frequencies of several substituted 2-pyrrolidinones using the TLSER and five additional experimentally derived solvent scale methodologies.


Famini et al.183 used TLSER methodology to correlate, illuminate, and probe eight solvent scales commonly used in LFER and physical organic chemistry. The data set consists of 30 common solvents. On the basis of the correlations obtained for these solvent scales, the Reichardt ENT (R ) 0.961), the Swain acidity, E (R ) 0.956), and basicity, B (R ) 0.928), the Koppel-Palm polarity, Y (R ) 0.914), and polarizability, P (R ) 0.925), the molar refraction, MR (R ) 0.975), and the Gutmann acceptor number, AN (R ) 0.972), and donor number, DN (R ) 0.917), the authors concluded that the TLSER method can predict values for these solvent scales and provide better understanding of the underlying physical meaning of these solvent scales. Carr and co-workers206 examined a number of empirical single-parameter scales of solvent strength (π*, ET) used to correlate solvatochromic phenomena in aprotic liquids considering the effects of modeling dipole-dipole and dipole-induced dipole interactions with a single global parameter while excluding the possibility of H-bonding interactions. They concluded that the regression coefficients are often misleading and not representative of the physical system. Some years later, on the basis of the study of the relationships between the solute capacity factor and Reichardt’s ET or the Kamlet-Taft π* scale in hydroorganic mixtures for a series of alkylbenzenes, Cheong and Carr207 showed that at least two solvent parameters are needed to account for the cavity formation and solute-solvent interaction processes which control retention in reversed-phase liquid chromatography. Shmidt, Mezhov, and Khananashvili compared the VR* (solvent influence) scale with (i) the empirical parameter scales developed for quantitative description of solvent characteristics (from LFER, solvent effects on chemical equilibrium, or solvent effects on reaction kinetics)208 and (ii) Kamlet-Taft spectrophotometric π* parameters, H2O solubilities in immiscible organic solvents, and H2O-solvent interfacial tensions. On the basis of these studies, the authors concluded that (i) the VR* parameter correlates linearly with the parameters of 20 other scales in the absence of specific solvation effects and (ii) the interfacial tensions could be predicted from VR* and π* parameters. Using several dyes, Spange and co-workers209 estimated the empirical donor-acceptor and polarity parameters of several inorganic solids, polymers, and combinations of both on the basis of a correlation analysis of the UV-vis spectral data of the probe dyes in more than 70 protonic and nonprotonic solvents versus the acceptor number of Gutmann and the Kamlet-Taft R, β, and π* solvatochromic parameters. Spange210 concluded that empirical polarity parameters are recommended as useful characteristics for describing the internal and external surface properties of various solid materials, for example, synthetic polymers, native polymers, inorganic oxides, sol-gel hybrids, and composites; a general polarity scale for solid materials, based on LSER study, is suggested. The Florida-Tartu group211 developed a threeparameter QSPR model (N ) 25 solvents, R2 ) 0.936), and Mu and Drago212 developed a two-


parameter MQSPR (model-based QSPR) model for a unified solvent polarity scale (S′) on the basis of theoretical molecular descriptors, calculated using CODESSA software. The descriptors utilized in these models provide insight into the solvation process at the molecular level. Katritzky and co-workers used the three-parameter model to extend available S′ values to a total of 67 solvents. Zou and co-workers213-215 performed ab initio calculations at the HF/6-31G* level for different data sets of solvents. The authors established linear correlations between ETN, π*, Py, SPP, S′, solvent softness scales, and theoretical descriptors by using multiple regression. These correlations have been analyzed from the point of view of intermolecular interactions between the “probe solute” and the solvent. On the basis of a stepwise correlation analysis, Berthelot et al.216 showed that the hydrogen-bond acceptor strengths of numerous bases can be formed from octanol-water partition coefficients after subtraction of a hydrophobic cavity term proportional to the molecular volume of the solutes. When one of the basic centers of the solute is hindered by bulky substituents, they observed significant deviations from the resulting two-parameter model. In an extensive attempt to relate solvent scales to the theoretical descriptors, the Florida-Tartu group217 used the CODESSA software to perform a quantitative structure-property relationship (QSPR) analysis of 45 different solvent scales and 350 solvents. In the attempt to obtain the optimum QSPR correlation results, scales were treated in the form of various mathematical functions: X-1, X2, X-2, X1/2, X-1/2, X3, X-3, and log(X). For example, scales Y, SB, d, J, BB, CB, E*MLCT, Dπ, and SPPN were found to be best correlated as Y2, SB2-, log(d), J2, BB3, CB2-, (E*MLCT)3, Dπ3, and (SPPN)3, respectively. The QSPR equations for the 45 scales treated contained altogether 118 different descriptors. Of course, some of these descriptors are very similar; for example, they can depend on the same intrinsic property of a solvent and differ only in their calculation methods, or they may derive from alternative semiempirical quantum chemical or empirical (Zefirov’s) methods of calculation of the charge distribution in the molecule. Therefore, the number of independent descriptors is actually far less than 118, but in this work no attempt was made to reduce the number of descriptors by substitution of one descriptor for another similar one. The high quality of the models (32 of the 45 give R2 > 0.90, whereas only two have R2 < 0.82) made possible direct calculation of predicted values for any of these scales for previously unmeasured solvents. The authors showed that in most cases the theoretical descriptors involved are in good agreement with the physical concepts invoked by the original authors of the scales. Chemometrics, or multivariate statistical analysis, is one of the most recent tools in attempts to relate solvent scales to descriptors. Eliasson et al.218 performed a multivariate analysis on the correlation between different solvent scales


and solvent-induced 13C NMR chemical shifts of a planar lithium carbanion. Auhmani et al.219 compared the empirical and chemometric approaches to the modeling of the solvent effects (Kamlet-Taft’s π*, R, and β parameters, ETN of Reichardt, and A and B of Swain) on a number of NMR, IR, and UV-vis spectral properties. They concluded that the correlations have a satisfactory quality. All of these studies indicated that the approach of relating solvent scales to different descriptors (i.e., LSER, TLSER, theoretical molecular descriptors, etc.) could finally lead to a more or less general solvent scale.

3. Interrelations between Solvent Scales Considering the vast number of existing single- and multiple-parameter solvent polarity scales, the question of their interrelations inevitably arises. The number of independent physical parameters describing solvent-dependent processes must be limited. Consequently, most scales should be highly intercorrelated; it follows that it should be possible to describe any individual solvent polarity scale using one or several other scales.

3.1. Correlation of Solvent Scales Comparing the solvent scales with each other may not be as trivial as it first could seem. For instance, many scales have been constructed for a rather limited range of solvents. Many probes can be used only in certain types of solvents: in one solvent they could be insoluble, unstable, or enter into undesirable side reactions. Several authors have used a combination of probes or extrapolation to overcome this difficulty and to get a reasonably extensive and, therefore, a generally applicable solvent scale. Another hindrance for the comparison of solvent scales is the range of their values. Many scales were proposed in a normalized form (typically between the values 0 and 1); others were presented the same way as they came from their respective equations or were normalized between some other boundaries. Thus, before any comparison or statistical analysis of solvent scales, they should desirably be normalized around some predefined value. In many cases, authors presenting a new study of some solvent-dependent process, which might find use as a solvent scale, compare and correlate their data with some well-known solvent polarity scale. Usually a limited number of other scales are considered, and frequently there are too few solvents common to the different scales to make the comparisons completely clear and reliable. Several authors have correlated one or two scales against some other scale; we mention only a selection of these studies, concentrating of the more extensive correlations available. Frequently, the analysis of scales taken from different sources does not result in high correlations. One reason can be the choice of solvents. Two solvent parameters may have a high correlation coefficient when a single family of solvents is considered (hy-

Katritzky et al.

drogen-bond donors, or electron pair donors, or nonpolar aprotic, etc.). However, two or three lines may be obtained, which can be parallel, crossing, or even orthogonal when the whole range of solvents is considered.220 A good correlation between two solvent scales means that the blend of different interaction forces between the solvent and the solute must be similar. In the case of a diverse set of solvents and mismatching solvent scales, the relationship could be something other than linear, for example, logarithmic. Earlier attempts to intercorrelate solvent scales are reviewed in a comprehensive study by Griffiths and Pugh.220 These authors analyzed correlations of the ET and Z scales. They compared the predicted Z values with those they measured themselves: 10 of the 16 solvents had the calculated value within 2% of the observed value with the rest also being reasonably close. They concluded that by using good linear correlations, nonmeasured or immeasurable solvent scale values could be calculated reliably. Analysis of relationships between the ET scale and other scales and solvent-dependent processes presented by Reichardt3 shows good correlations for several processes, especially for non-hydrogen-bond donor solvents. Redondo et al.221 examined the G scale in detail and correlated the values of 36 solvents (also separately nonhydroxylic and nonacidic solvents) with the ET scale, Koppel and Palm parameters (Y, P, and E), and Kamelt and Taft parameters (π* and R). They found the Kamlet and Taft treatment to be superior to others and appropriate to predict nonmeasurable values for the G scale. They concluded that the G scale is a measure of the combination of solvent polarity-polarizability (π* and P + Y) and acidity (E and R). Buncel and Rajagopal49 compared their π*azo scale with the π* scale for the ability to describe the variation in other polarity scales. They found that the π*azo scale is slightly better for the overall description of solute-solvent interactions than the popular π* scale, except for aromatic nitro compounds (the primary solute type for the π* scale). Their correlation shows that the π*azo scale based on azo merocyanines correlates better with (i) scales based on structurally similar dyes and (ii) dyes that are structurally similar to azo merocyanines.50 A comprehensive study and a detailed analysis of series of Lewis basicity (electron pair donating) scales were carried out by Sandstro¨m et al.195 Correlations with their DS scale as well as between other scales are presented and discussed. They stressed the importance of the softness/hardness concept in donoracceptor interactions. They often found a nonlinear (e.g., logarithmic) dependence between soft acceptor and hard acceptor based basicity scales. Several inconsistencies and shortcomings in basicity scales were analyzed. Hard acceptor based scales are more common and correlate well among themselves. The use of ∆HBF3 as a hard donor scale is recommended over DN, Cu λmax, and CP. The best overall soft donor scale was found to be DS over µ, Bsoft, and SP. Hydrogen-bond acceptor properties were found to be


well described by the β1 scale and, in specific cases, the log Kβ and βsm scales. Other basicity scales (multiparameter scale E and C, ∆δ) were found to have rather limited use. Sometimes, careful correlation analysis of several solvent scales reveals experimental or derivational shortcomings for some data points. Water is a solvent of unique chemical nature; solvent polarity values for water are frequently obtained indirectly, by extrapolation from data of binary mixtures, or by using other probes, or by correlation with other similar scales. For instance, the Z value of water (94.6) was analyzed by Griffiths and Pugh220 and found to be too large; correlations with other scales (Y and ∆R) suggested a lower value by some 3 kcal/mol. It could prove useful to remeasure the values of widely used scales proposed many years ago before any correlation analysis and statistical expansion of these scales is done as experimental techniques and equipment have often much improved since.

3.2. Overall Dimensionality of Solvent Parameters There are several possible statistical approaches for the analysis and reduction of the dimensionality of solvent scales.

3.2.1. General Statistical Approaches One of the simplest approaches is to test all proposed “general” multiparameter scales to verify their ability to fit the data of all the other scales. In general, this is already carried out in the course of establishing each new scale (by correlating with several other known scales), and the information from this approach is already available. Another treatment is pairwise linear correlation analysis between each of the individual scales to find out the most and least intercorrelated ones: this groups scales according to their interrelation and, thus, indicates the most relevant elements of solvent effects for each scales. Also, any scale with all intercorrelations below some predefined threshold value can then be considered to represent a new independent solvent parameter, not sufficiently described by any other scales. Marcus14 studied nine solvent parameters, R, β, π*, ET(30), DN, AN, Z, acidity, and basicity, and found several to be highly interrelated. He concluded that there were four essentially independent solvent parameters: hydrogen-bond donation ability (described best by R), hydrogen-bond acceptor ability (β), polarity/polarizability (π*), and solvent stiffness (δH2). Sergent et al.222,223 developed an “informative” approach, an optimum design methodology, to compare two empirical sets of solvent scales, those of Koppel and Palm (KP) and of Kamlet, Abboud, and Taft (KAT), with the purpose to determine if they are identical, similar, or quite distinct. The experimental results used in the comparison were the keto/enol equilibrium constants of 2,4-pentanedione determined by 1H NMR spectroscopy. The conclusion was that both sets of scales are similar, one being more precise (KP) and the other more robust (KAT). Catalań122 found a significant correlation between the SPP scale and the π* scale by Kamlet, Abboud,


and Taft for a set of 67 solvents. He also correlated the EpNA scale224 with five other well-known solvent scales [ET(30), π*, Py, S′, and SPP].225 The work of Famini and Wilson183 of the application of the TLSER methodology was discussed in the previous section. Malavolta et al.226 analyzed various polarity scales and their linear combinations for about 50 solvents in terms of the sum of Gutmann’s donor and acceptor numbers (AN + DN). No correlation was obtained with Hildebrand’s solubility parameter, δ, and Kamlet-Taft’s π* scale. A moderate correlation was found between AN + DN and the solvatochromic ET(30) scale (r ) 0.7374). Notably, the best correlation was found with the combination of Kamlet-Taft’s parameters R + β (r ) 0.9251), indicating considerable similarity. Mancini et al.227 have analyzed the relationship between different solvatochromic polarity scales (π*OMe, π*NMe2, π*2, and ETN) in a number of binary solvent mixtures: they found significant two-parameter correlations for π*OMe and π*NMe2 with π*2 and ETN. This result is not unexpected because of the similarity of indicator processes used in the definition of the respective scales. Palm and Palm chose a different approach in their study of the total number of independent variables for solvent-dependent processes. They picked a small initial set of “fundamental” scales and extended it by means of the SMIRC procedure228 to include nine “purified” solvent parameter scales; later they reduced their model to eight parameters, claiming that it accounted for all of the dimensionality of solventdependent processes. The authors concluded that the stability of their results indicates a rather universal applicability and sufficiency of this set of solvent parameters. Their treatment found Y, P, δH2, B, ET(30), π*, β, and R to be statistically significant; their residual scales are somewhat different from the original ones due to the purification process. An extensive set of 359 solvent-dependent processes was then correlated using their model229,230 with rather good results.

3.2.2. Principal Component Analysis (PCA) Approach Another option for treating this type of dimensionality and interrelation questions is the conventional PCA. Chastrette and Carretto applied PCA to analyze231 and to calculate empirical parameters of solvent polarity starting with the physicochemical properties of the solvents;232 Chastrette and coworkers233 used multivariate statistical treatment to classify 83 solvents using eight solvent parameters (K, MR, δ, µ, nD, bp, H, and L), but their focus was mainly on the grouping of solvents rather than solvent scales. Nevertheless, from the intercorrelation of the solvent parameters they concluded that fewer than eight parameters should be sufficient to describe the whole dimensionality. Maria et al.234 studied the basicity-dependent behavior in the condensed phase of nonprotogenic organic molecules commonly used as solvents. PCA of a set of basicity-dependent properties was applied to hydrogen-bonding, proton-transfer, and interactions with hard and soft Lewis acids, including the -∆H°BF3 basicity scale. One of the conclusions was


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Figure 1. Loadings of the second PCA component plotted versus the loadings of the first component with the third component loading and scale classification given as labels to the data points. b, ×, 0, and 4 represent R g 90%, 80 e R < 90%, 70 e R < 80%, and 54 e R < 70%, respectively. (Reproduced with permission from J. Chem. Inf. Comput. Sci. 1999, 39, 692. Copyright 1999 American Chemical Society.)

that the Kamlet-Taft β parameter is a good descriptor of the Gibbs free energies of hydrogen bonding. A common hindrance to the application of all statistical methods, for the analysis of the dimensionality and the interrelation of the solvent scales, is the large number of missing values. PCA, for instance, requires a completely filled data matrix. Several methods can be used to deal with this problem. The simplest would be to exclude all scales and solvents for which there are insufficient data, but this approach leaves only a very small data matrix. It is preferable to predict the missing values, which can be done either using other highly intercorrelated scales (as was done by Palm and Palm) or from QSPR models built for each scale. The last approach was chosen by the FloridaTartu group,235 who developed a complete data matrix for 40 scales by 40 solvents. To overcome the incompleteness of experimental data in the respective matrix, each scale was correlated with CODESSA descriptors to predict the missing scale values.217 Their QSPR approach was already discussed under section 2.4. Following the CODESSA treatment, 40 scales involving 40 solvents were selected for the subsequent PCA analysis. PCA allows the examination of a set of characteristics (variables) of a class of compounds (objects) to

investigate the relations between them. It enables the identification of one, two, three, or more principal components (PCs) derived from the characteristics for the compounds examined. These components have defined values for each of the compounds (t1i, t2i, and t3i, the “scores”) and are taken in certain proportions (p1k, p2k, p3k, etc., the “loadings”) for each type of characteristic. Graphical representations of these values, the “scores” plot for the compounds and the “loadings” plot for the characteristics, provide pictures that allow the recognition of systematic patterns that are otherwise difficult to deduce from the original data matrix. On the basis of the full 40 × 40 matrix, it was found235 that most of the variation (>74%) in the data was described by just three principal components, whereas six components account for 90% of the variance. The loadings of the first three components divide the scales into seven distinct groups (Figure 1). Those groups are characterized as follows:235 (i) The five scales J, S′, d, Y, and N have large positive loadings (0.85-0.94) for the first component, small positive loadings (0.16-0.40) for the second component, and small loadings (-0.14 to 0.11) for the third component. These scales depend heavily on the solvent dielectric constant.


(ii) The 13 scales ET, S, ECT(A), AN, A, EB, Z, E, ETSO, SA, R, γ, and CB have large positive loadings (0.490.97) for the first component, small to medium negative loadings (-0.11 to -0.55) for the second component, and relatively small loadings (-0.48 to 0.02) for the third component. Most of these scales are highly influenced by the solvent stabilization of charge transfer in the UV-vis absorption spectral maximum of large and highly polarized conjugated systems. According to the findings from the CODESSA treatment, these scales reflect mainly the acidic and electrophilic properties of solvents. (iii) The seven scales BB, PS, π*, Py, E*MLCT, EBB, and SPPN display medium to large positive loadings for the first (0.51-0.69) and second components (0.46-0.72) and small loadings (-0.41 to 0.20) for the third component. Most of these scales measure the ability of the solvent to change a UV absorption maximum, but unlike group ii these scales account more for nonspecific solvent dipole effects. (iv) The nine scales B-2, ∆H0BF3, DS, DN, Dπ, π*aso, ∆νOH, B, and β show small to moderate positive loadings (0.07-0.59) for the first component, small loadings (-0.06 to 0.26) for the second component, and large positive loadings (0.50-0.91) for the third component (except for the loading of π*aso, which is -0.41). These scales reflect solvent basicity. (v) Scale SB is unique with a small negative first component and medium negative second (-0.62) and third components (-0.48). The SB scale can be used to describe solvent basicity effects based on experimental evidence from UV-vis spectroscopy. Apparently, this scale includes some specific solvent influence not well understood. (vi) The four scales P, M, µ, and ∆νCl have medium negative first components (-0.31 to -0.504), medium positive second components (0.40-0.54), and small to medium positive or negative third components (-0.45 to 0.26). These scales mainly reflect the solvent refractive index (polarizability) and describe the softness of solvents. (vii) Scale χR has a large negative first component (-0.85), a small negative second component (-0.26), and a small positive third component (0.22). This scale is based on the transition energy of merocyanine dyes. Significantly, 34 of the 40 scales used in the PCA treatment235 are concentrated into four major groups, i-iv. This is the same dimensionality of solvent effects as was suggested in 1972 by Koppel and Palm9 on the basis of their classic analysis of the experimental data. Thus, these 34 results support their observation. However, the remaining six scales of groups v-vii deviate significantly in the PCA loadings. Notably, as a result of the PCA treatment of the 40 × 40 matrix,235 the solvents also showed clear clustering into five groups: (i) Formamide has a very large positive score (2.02) for the first component and a medium positive score (0.59) and a small negative score (-0.26) for the second and third components, respectively. It is highly polar and can form both intermolecular and


intramolecular hydrogen bonds, which distinguishes it from the solvents in group iii. (ii) The nine hydroxylic solvents have moderate to large positive scores (water 3.14, others 0.32-1.36) for the first component and moderate to large negative scores (water -2.69, others -0.45 to -1.15) for the second component, together with variable scores (-1.39 to 1.01) for the third component. The very high first- and second-component scores separate water from the alcohols. The solvents of this group are all highly polar protic solvents, and all form strong hydrogen bonds. (iii) The 12 dipolar aprotic solvents, which are strong H-bond acceptors but not donors, have small negative to medium positive scores (-0.09 to 0.68) for the first component, medium to large positive scores for the second component (0.48-1.80), and highly variable scores (-1.45 to 0.97) for the third component. (iv) The ethers, esters, amine, alkyl halides, and five aromatic-ring-containing solvents have small to large negative scores (-0.32 to -1.21) for the first component, moderate negative to moderate positive scores (-0.61 to 0.34) for the second component, and very variable scores (-1.85 to 2.92) for the third component. These solvents possess polarity notably smaller than the solvents in groups ii and iii, but notably larger than those in group v. (v) n-Hexane, cyclohexane, and carbon tetrachloride are distinct from other solvents with large negative scores for the first (-1.45 to -1.72) and second components (-1.25 to -1.69) and medium positive (0.32-0.41) or large negative scores (-2.25) for the third component. These three solvents are all apolar. The PCA score grouping directly reflects the chemical nature of the solvents. Specifically, the solvents from the set of 40 fall into six distinct groups representing solvent classes from highly polar protic solvents (acetic acid and water) to apolar alkanes (nhexane). PCA and multivariate methods have both their advantages and weaknesses. Principal components have the built-in advantage of being mutually orthogonal, as compared to the sometimes highly intercorrelated nature of solvent scales. The most fundamental shortcoming of principal components is their lack of physicochemical correspondence to any theoretically derived property; the loadings are purely mathematical entities. The same can be said about purified solvent parameters that are obtained by subtracting the parts described by other parameters. Finally, it is quite possible that all of the various physicochemical aspects of solvent-solute interaction are NOT orthogonal. Thus, acidity and electron pair donor properties likely depend on dipolarity and polarizability. Thus, residual descriptors could be very refined but lack any commonly understood names. Possibly we have to choose between orthogonality and good meaningful physicochemical parameters. To describe meaningfully separate types of interaction, one should use carefully chosen solvent parameters, whereas if the best overall fit and


dimensionality are important, one should stick to orthogonal principal components or residual descriptors. It is important to note that in most cases all treatments reveal high intercorrelation among various acidity (hydrogen-bond donor) scales. Reasonably distinct groups of scales are made up of nonspecific dipolarity, polarizability, and dielectric constant based scales. Basicity (hydrogen-bond acceptor) scales appear to have much larger variety, apparently due to the softness-hardness factor and the somewhat specific nature of electron donor sites. All of the treatments also appear to point in the same direction: although very many solvent polarity scales are highly interrelated and most of the scales can be grouped into some five large families, the whole variance in solvent-dependent processes cannot be accounted for using even as many as 9 or 10 parameters.

4. Summary and Future Work As described above, major efforts have been made to develop quantitative scales and models to describe the solvent effects on chemical reactivity and physical properties of compounds in condensed media. It is essential to distinguish between two objectives that trigger those studies but that may lead to contradictory goals or conclusions from the research carried out. On the one hand, from the utilitarian point of view, it would be ideal to find a universal set of parameters that enable the quantitative prediction of the effects of solvent on as wide as possible a selection of physical, chemical, biological, and technological processes of solvents, and, on the other hand, it would be important to understand thoroughly the relationship between the different solvent parameters and the physical interactions between solute and solvent molecules. It is not obvious that the “best” set of parameters in the statistical sense would be the best to differentiate between individual physical interactions between solute and solvent. Of course, most empirical solvent effect scales have been developed proceeding from some theoretical concepts about the intermolecular interactions in condensed media. In other words, the scales based on certain macroscopic experimental data are often related to individual, physically distinct mechanisms of solvation at the microscopic molecular level. Unfortunately, different experimentally observable chemical and physical processes are influenced, as a rule, simultaneously by several solute-solvent interactions in solution. The different mechanisms of interaction have, in general, a different relative importance in their influence on different experimental molecular properties in solution; thus, such “mixed” empirical solvent effect scales cannot be expected to be universally applicable. In addition, the cooperative effects (e.g., the restrictions to the polarization due to hydrogen bonding) may bring up nonlinear dependencies of observable properties from solvent scales defined using some standard process or measurable quantity. One possible formal way to account for such nonlinearities would be the use of so-called “cross-terms” in the model development, introduced

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as the products of different scales. Notably, this approach has been used very rarely in the description of solvent effects, but it could have some value if a formal model for a wide spectrum of solvents is aimed for. Another approach that would possibly help to elucidate further the content of different empirical solvent effect scales would be the PCA and QSPR treatment of these scales together with various theoretically calculated contributions to the free energy of solvation. Those contributions correspond conventionally to the electrostatic and dispersion interactions between the molecules in condensed media and involve also the effects related to the cavity formation and solvent reorganization.236-241 Such analysis would be particularly useful for the attempts to develop new, universally applicable theoretical descriptors for solvent effects. Last but not least, it must be emphasized the present solvent polarity scales are mostly derived for pure solvents. However, a large part of chemistry and many natural processes are carried out in mixtures of solvents. Therefore, it would be of much practical importance to extend the solvent scales and the corresponding QSPR models to multicomponent systems.

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